We present a novel method for simulating the noisy behavior of quantum computers, which allows to efficiently incorporate environmental effects in the driven evolution implementing the gates acting on the qubits. We show how to modify the noiseless gate executed by the computer to include any Markovian noise, hence resulting in what we will call a noisy gate. We compare our method with the IBM qiskit simulator, and show that it follows more closely both the analytical solution of the Lindblad equation as well as the behavior of a real quantum computer, where we ran algorithms involving up to 18 qubits; as such, our protocol offers a more accurate simulator for NISQ devices. The method is flexible enough to potentially describe any noise, including non-Markovian ones. The noise simulator based on this work is available as a python package at the link, https://pypi.org/project/quantum-gates.
We present a novel method for simulating the noisy behavior of quantum computers, which allows to efficiently incorporate environmental effects in the driven evolution implementing the gates acting on the qubits. We show how to modify the noiseless gate executed by the computer to include any Markovian noise, hence resulting in what we will call a noisy gate. We compare our method with the IBM qiskit simulator, and show that it follows more closely both the analytical solution of the Lindblad equation as well as the behavior of a real quantum computer, where we ran algorithms involving up to 18 qubits; as such, our protocol offers a more accurate simulator for NISQ devices. The method is flexible enough to potentially describe any noise, including non-Markovian ones. The noise simulator based on this work is available as a python package at the link, https://pypi.org/project/quantum-gates.
Abstract This practical guide presents methods for constructing noise models using the Qiskit Aer noise module within the IBM Q ecosystem. The objective is to simulate quantum circuits under realistic error conditions, enabling accurate emulation of noisy quantum processors. The guide demonstrates how to: Use the Qiskit Aer noise module to define custom noise models. Incorporate gate errors, readout errors, and decoherence effects into simulations. Apply noise channels (e.g., depolarizing, amplitude damping, phase damping). Attach noise models to quantum circuit simulations. Analyze how noise affects algorithm performance and output distributions. Building noise models is essential for studying the behavior of quantum algorithms in the NISQ (Noisy Intermediate-Scale Quantum) era. It allows researchers to evaluate algorithm robustness, optimize circuit depth, and test error mitigation strategies before execution on real IBM Quantum hardware. This approach provides a bridge between ideal theoretical circuits and physically realistic quantum devices, enhancing the reliability and applicability of quantum computing experiments.
The study of the impact of noise on quantum circuits is especially relevant to guide the progress of Noisy Intermediate-Scale Quantum (NISQ) computing. In this paper, we address the pulse-level simulation of noisy quantum circuits with the Quantum Toolbox in Python (QuTiP). We introduce new tools in qutip-qip , QuTiP's quantum information processing package. These tools simulate quantum circuits at the pulse level, leveraging QuTiP's quantum dynamics solvers and control optimization features. We show how quantum circuits can be compiled on simulated processors, with control pulses acting on a target Hamiltonian that describes the unitary evolution of the physical qubits. Various types of noise can be introduced based on the physical model, e.g., by simulating the Lindblad density-matrix dynamics or Monte Carlo quantum trajectories. In particular, the user can define environment-induced decoherence at the processor level and include noise simulation at the level of control pulses. We illustrate how the Deutsch-Jozsa algorithm is compiled and executed on a superconducting-qubit-based processor, on a spin-chain-based processor and using control optimization algorithms. We also show how to easily reproduce experimental results on cross-talk noise in an ion-based processor, and how a Ramsey experiment can be modeled with Lindblad dynamics. Finally, we illustrate how to integrate these features with other software frameworks.
Noise in quantum devices is generally considered detrimental to computational accuracy. However, the recent proposal of noise-assisted simulation has demonstrated that noise can be an asset in digital quantum simulations of open systems on noisy intermediate-scale quantum (NISQ) devices. In this context, we introduce an optimized decoherence rate control scheme that can significantly reduce computational requirements by multiple orders of magnitude, in comparison to the original noise-assisted simulation. We further extend this approach to encompass Lindblad equations with time-dependent coefficients, using only quantum error characterization and mitigation techniques. This extension allows for the perturbative simulation of non-Markovian dynamics on NISQ devices, eliminating the need for ancilla qubits or midcircuit measurements. Our contributions are validated through numerical experiments on an emulated IBM Quantum device. Overall, our paper offers valuable optimizations that bring current quantum processors closer to effectively simulating realistic open systems.
A major problem in exploiting microscopic systems for developing a new technology based on the principles of quantum information is the influence of noise, which tends to work against the quantum features of such systems. It thus becomes crucial to understand how noise affects the evolution of quantum circuits: several techniques have been proposed, among which stochastic differential equations (SDEs) can represent a very convenient tool. We show how SDEs naturally map any Markovian noise into a linear operator, which we call a noise gate, acting on the wave function describing the state of the circuit, and we discuss some examples. We show that these gates can be manipulated like any standard quantum gate, thus simplifying in certain circumstances the task of computing the overall effect of the noise at each stage of the protocol. This approach yields equivalent results to those derived from the Lindblad equation; yet, as we show, it represents a handy and fast tool for performing computations, and, moreover, it allows for fast numerical simulations and generalizations to non-Markovian noise. In detail we review the depolarizing channel and the generalized amplitude damping channel in terms of this noise gate formalism and show how these techniques can be applied to any quantum circuit.
Classical simulation of Noisy Intermediate Scale Quantum computers is a crucial task for testing the expected performance of real hardware. The standard approach, based on solving Schrödinger and Lindblad equations, is demanding when scaling the number of qubits in terms of both execution time and memory. In this article, attempts in defining compact models for the simulation of quantum hardware are proposed, ensuring results close to those obtained with standard formalism. Molecular Nuclear Magnetic Resonance quantum hardware is the target technology, where three non-ideality phenomena—common to other quantum technologies—are taken into account: decoherence, off-resonance qubit evolution, and undesired qubit-qubit residual interaction. A model for each non-ideality phenomenon is embedded into a MATLAB simulation infrastructure of noisy quantum computers. The accuracy of the models is tested on a benchmark of quantum circuits, in the expected operating ranges of quantum hardware. The corresponding outcomes are compared with those obtained via numeric integration of the Schrödinger equation and the Qiskit’s QASMSimulator. The achieved results give evidence that this work is a step forward towards the definition of compact models able to provide fast results close to those obtained with the traditional physical simulation strategies, thus paving the way for their integration into a classical simulator of quantum computers.
Quantum algorithms offer efficient solutions to computational problems that are expensive to solve classically. Publicly available quantum computers, such as those provided by IBM, can now be used to run small quantum circuits that execute quantum algorithms. However, these quantum computers are highly prone to noise. Here, we introduce important concepts of quantum circuit noise and connectivity that must be addressed to obtain reliable results on quantum computers. We utilize several examples to show how noise scales with circuit depth. We present Simon's algorithm, a quantum algorithm for solving a computational problem of the same name, explain how to implement it in IBM's Qiskit platform, and compare the results of running it both on a noiseless simulator and on physical hardware subject to noise. We discuss the impact of Qiskit's transpiler, which adapts ideal quantum circuits for physical hardware with limited connectivity between qubits. We show that even circuits of only a few qubits can have their success rate significantly reduced by quantum noise unless specific measures are taken to minimize its impact.